%   ORIGINAL: h4/rich__list/MEM__BUTLASTN
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/rich__list/MEM__EXISTS: !x l. h4/bool/IN x (h4/list/LIST__TO__SET l) <=> h4/list/EXISTS ($equals x) l
% Assm: h4/rich__list/EXISTS__BUTLASTN: !m l. h4/arithmetic/_3C_3D m (h4/list/LENGTH l) ==> (!P. h4/list/EXISTS P (h4/rich__list/BUTLASTN m l) ==> h4/list/EXISTS P l)
% Goal: !m l. h4/arithmetic/_3C_3D m (h4/list/LENGTH l) ==> (!x. h4/bool/IN x (h4/list/LIST__TO__SET (h4/rich__list/BUTLASTN m l)) ==> h4/bool/IN x (h4/list/LIST__TO__SET l))
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_richu_u_lists_MEMu_u_EXISTS]: !x l. h4/bool/IN x (h4/list/LIST__TO__SET l) <=> h4/list/EXISTS ($equals x) l
% Assm [h4s_richu_u_lists_EXISTSu_u_BUTLASTN]: !m l. h4/arithmetic/_3C_3D m (h4/list/LENGTH l) ==> (!P. h4/list/EXISTS P (h4/rich__list/BUTLASTN m l) ==> h4/list/EXISTS P l)
% Goal: !m l. h4/arithmetic/_3C_3D m (h4/list/LENGTH l) ==> (!x. h4/bool/IN x (h4/list/LIST__TO__SET (h4/rich__list/BUTLASTN m l)) ==> h4/bool/IN x (h4/list/LIST__TO__SET l))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q162733,TV_Q162729]: ![V_f, V_g]: (![V_x]: s(TV_Q162729,happ(s(t_fun(TV_Q162733,TV_Q162729),V_f),s(TV_Q162733,V_x))) = s(TV_Q162729,happ(s(t_fun(TV_Q162733,TV_Q162729),V_g),s(TV_Q162733,V_x))) => s(t_fun(TV_Q162733,TV_Q162729),V_f) = s(t_fun(TV_Q162733,TV_Q162729),V_g))).
fof(ah4s_richu_u_lists_MEMu_u_EXISTS, axiom, ![TV_u_27a]: ![V_x, V_l]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),d_equals(s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_richu_u_lists_EXISTSu_u_BUTLASTN, axiom, ![TV_u_27a]: ![V_m, V_l]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => ![V_P]: (p(s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_butlastn(s(t_h4s_nums_num,V_m),s(t_h4s_lists_list(TV_u_27a),V_l)))))) => p(s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l))))))).
fof(ch4s_richu_u_lists_MEMu_u_BUTLASTN, conjecture, ![TV_u_27a]: ![V_m, V_l]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => ![V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_butlastn(s(t_h4s_nums_num,V_m),s(t_h4s_lists_list(TV_u_27a),V_l)))))))) => p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l))))))))).
